The Combinatorics, Coding and Security Group (CCSG) is a research group in the Department of Information and Communications Engineering (DEIC) at the Universitat Autònoma de Barcelona (UAB).
Group CCSG has been uninterruptedly working since 1987 in several projects and research activities on Information Theory, Communications, Coding Theory, Source Coding, Cryptography, Electronic Voting, Network Coding.
Our research group CCSG has been producing mainly results on optimal coding. Specifically, the research has been focused on uniformly-packed codes; perfect codes in the Hamming space; perfect codes in distance-regular graphs; the classification of optimal codes of a given length; and codes which are close to optimal codes by some properties, for example, Reed-Muller codes, Preparata codes, Kerdock codes and Hadamard codes.
Currently, the coding theory questions and problems we are dealing with can be divided into those more theoretical, with an structural and basic nature, and those more related to applications of error correcting codes aiming to solve specific engineering problems.
On one hand, the more theoretical topics on which our group is working are related to propelinear codes, transitive codes, etc. or, specifically, Preparata codes, Kerdock codes, Reed-Muller codes, Hadamard codes and Z2Z4-linear codes. Many variants of these codes are nonlinear and some of their structural parameters are unknown, for instance, their rank and their dimension of the kernel.
Other theoretical topics on which our group is also working and has obtained good results, are completely regular codes. Their classification and characterization are still unsolved and nowhere near reaching the end, but we are very focused on obtaining new families using techniques coming from algebraic combinatorics.
On the other hand, our group is also working on applications of some of the aforementioned coding theory problems to solve specific engineering problems. Specifically, on data hiding, whose goal is hiding information inside a cover object, usually an image; on documents authentication, where it is expected to know what fields have been compromised from a hash of the source file; and on the recovery of the information that has been stored in a distributed environment.
Moreover, the group is also developing software within the Magma system, which is currently the most efficient tool for simulating error correcting codes. In this sense, we are implementing new packages to work with nonlinear codes, with the double purpose of being able to analyze new optimal codes and to provide new research tools in the coding theory field.
In summary, the main research objectives in which our group is working on, include to:
- characterizate and construct new Z2Z4-linear codes, and compute their structural parameters;
- characterize and construct families of Z2Z4-linear Reed-Muller codes, and compute their rank and dimension of the kernel;
- characterize and construct new completely regular codes and compute their respective intersection array;
- construct transitive codes and study their relationship with propelinear codes;
- develop appropriated algorithms to establish new choices in data-hiding and documents authentication, using Z2Z4-linear codes;
- construct new families of systematic regenerating codes in order to minimize the code repair problem that appears when it is necessary to recover information stored in a distributed environment;
- propose new systems to guarantee data integrity and data authentication, using hash functions, classical error correcting codes and network coding;
- extend the Magma software system implementing new packages to work efficiently with Z2Z4-linear codes, completely regular codes, and nonlinear codes in general.
CCSG collaborates with other national and international research groups and is open to new collaborations with other researchers. A list of professors currently sharing some research with our group:
- Prof. Faina Soloveva del Sobolev Insititute of Mathematics of Siberian Division of the Russian Academy of Sciences.
- Prof. Victor Zinoviev del Institute of Information Transmission Problems (IITP) of the Russian Academy of Sciences.
- Prof. Kevin T. Phepls de Auburn University (USA).
- Prof. Helena Rifà-Pous del grupo KISON (Universitat Oberta de Catalunya).
- Prof. Steven Dougherty de University of Scranton (USA).
- Prof. Angel del Rio de la Universidad de Murcia, España.
CCSG is also interested in the supervision of Master and PhD Thesis under the official Graduate Programme on Computer Science, and in
the tuition of undergraduate degree projects for UAB students. To retrieve more information, please visit our section Join Us or contact us at:
Keywords: Information coding (Error-correcting codes, Completely Regular Codes, Perfect Codes, Z2Z4-linear Codes, network coding); Distributed storage (regenerating codes, data authentication, data integrity, data hiding); Magma software system (algorithms for nonlinear codes, algorithms for Z2Z4-linear codes).